Pricing Critical Illness Insurance from Prevalence Rates: Gompertz versus Weibull

The pricing of a Critical Illness insurance requires specific and detailed insur- ance data on healthy and ill lives. However, where the Critical Illness insurance market is small or national commercial insurance data needed for premium esti- mates is unavailable, national health statistics can be a viable starting point for insurance ratemaking purposes, even if such statistics cover the general popu- lation, are aggregate and are reported at irregular intervals. To develop a Critical Illness insurance pricing model structured on a multiple state continuous and time- inhomogeneous Markov chain and based on national statistics, we do three things: First, assuming that the mortality intensity of healthy and ill lives is modeled by two parametrically different Weibull hazard functions, we provide closed formu- las for transition probabilities involved in the multiple state model we propose. Second, we use a data set that allows us to assess the accuracy of our multiple state model as a good estimator of incidence rates under the Weibull assumption applied to mortality rates. Third, the Weibull results are compared to correspond- ing results obtained by substituting two parametrically different Gompertz models for the Weibull models of mortality rates, as proposed in Baione and Levantesi (2014). This enables us to assess which of the two parametric models is the supe- rior tool for accurately calculating the multiple state model transition probabilities and assessing the comparative efficiency of Weibull and Gompertz as methods for pricing Critical Illness insurance.